CN107515956A - A kind of large-scale finite plane array analysis method based on HFSS elements methods - Google Patents
A kind of large-scale finite plane array analysis method based on HFSS elements methods Download PDFInfo
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Abstract
The invention discloses a kind of large-scale finite plane array analysis method based on HFSS elements methods, comprise the following steps：HFSS elements methods are analyzed：Unlimited Array Model is established using HFSS elements methods, and phase difference principal and subordinate's border surface is sampled, emulation obtains the infinite matrix active refelction coefficient of each sampled point in a complete cycle structure；Coupling analysis：The Mutual Coupling Analysis that array is realized in Fourier transform is done to the infinite matrix active refelction coefficient under different sampled points, determines the coupling S parameter of infinite matrix；Active cell Directional Pattern Analysis：According to active cell directional diagram and the relation for coupling S parameter, active cell directional diagram is determined with reference to independent array element directional diagram, the element position of limited battle array, width phase information；Array pattern integrates and amendment：Integrated active element pattern, and synthesis result is modified and finally gives synthesized pattern.Simulation velocity of the present invention is fast, precision is high, supports any width of each unit mutually to encourage, can realize the Mutual Coupling Analysis and Pattern Synthesis of extensive planar array.
Description
Technical field
The present invention relates to array antenna simulation technical field, particularly a kind of large-scale finite plane based on HFSS elements methods
Array analysis method.
Background technology
The accurate analysis of array antenna grades numerical algorithm generally by means of moment method, FInite Element, Finite Difference-Time Domain, so
And the limitation of current computer computing capability is limited to, once array scale is excessive, the synthesis of directional diagram will be difficult to, and base
In the electromagnetic simulation software of these algorithms, such as HFSS, CST, full array modeling and simulation also will can not be equally realized.Now,
To the comprehensive analysis of array pattern, often directly one is obtained simply using the antenna pattern product theorem of classical approach
As a result.But after antenna array, mutual coupling can be produced between each unit；The edge of antenna array can also have the edges such as the diffraction of field effect
Should, be present larger difference in the directional diagram under this directional diagram and truth for obtain based on classical approach, therefore, find a kind of
The method of simple and fast and accurate large-scale array analysis is particularly important.
Based on the purpose of Simplified analysis process, scientists just propose the concept of unlimited array.Unlimited array is exactly false
If center array element is as surrounding infinite expanding in a manner of structuring the formation accordingly, the position relationship of each array element is complete in so unlimited array
It is identical.HFSS elements methods are exactly that a kind of large-scale Finite Array analysis method this method based on infinite matrix concept models to array
When only include an antenna element, and according to group corresponding periodic boundary condition of battle array formal definition, it is unlimited to be used for simulating
Array, but this method does not consider two secondary couplings and edge effect, larger error be present in the synthesized pattern for emulating to obtain；And not
Support any width of each unit mutually to encourage, can only obtain array synthetic directional diagram, array coupling parameter and unit radiation can not be obtained
Directional diagram.
The content of the invention
It is an object of the invention to provide a kind of simple and fast, accuracy are high large-scale limited flat based on HFSS elements methods
Face array analysis method, to realize the Mutual Coupling Analysis and Pattern Synthesis of large-scale limited planar array.
Realize that the technical solution of the object of the invention is as follows：A kind of large-scale finite plane array based on HFSS elements methods
Analysis method, step are as follows：
Step 1, HFSS elements methods are analyzed：Unlimited Array Model is established using HFSS elements methods, and to principal and subordinate's border surface
Between phase difference sample, emulation obtain the infinite matrix active refelction coefficient of each sampled point in a complete cycle structure；
Step 2, coupling analysis：Fourier transform is done to the infinite matrix active refelction coefficient under different sampled points and realizes array
Mutual Coupling Analysis, determine the coupling S parameter of infinite matrix；
Step 3, active cell Directional Pattern Analysis：According to active cell directional diagram and the relation for coupling S parameter, with reference to independence
Array element directional diagram, the element position of limited battle array, width phase information determine active cell directional diagram；
Step 4, array pattern synthesis and amendment：Integrated active element pattern, and synthesis result is modified most
Synthesized pattern is obtained eventually.
Further, HFSS elements methods described in step 1 are analyzed, specific as follows：
(1.1) unlimited Array Model is established using HFSS elements methods：Single array element is built in electromagnetic simulation software HFSS
Mould, add two pairs of principal and subordinate borders to forcing field duration property to realize the infinite matrix model of planar array along array grid direction；
(1.2) phase difference p principal and subordinate's border surface in both direction1、p2Carry out N*N point samplings：
(1.3) emulated to obtain using the method for MATLAB-HFSS associative simulations different in a complete cycle structure
Infinite matrix active refelction coefficient under sampled point
Further, the detailed process of coupling analysis described in step 2 is as follows：
To the infinite matrix active refelction coefficient under different sampled pointsTwo-dimension fourier transform is done, it is unlimited to obtain
The coupling S parameter of battle array
Wherein, δ1、δ2Represent respectively along the phase difference between the adjacent array element in array grid both direction, p, q difference table
Showing p-th of the array element and q-th of array element along distance reference array element in array grid both direction, N represents sampling number, wherein
Further, active cell Directional Pattern Analysis described in step 3, it is specific as follows：
For the limited big planar array of a M array element, the field strength of the pumping signal of M unit is a in arrayi, i=
1,2 ..., M, consider the mutual coupling between each antenna element, the reflected signal field strength b of kth unitkIt is expressed as：
In formula, SkiIt is to reflect the mutual coupling coefficient that i-th cell influences on kth unit；The active refelction coefficient definition of kth unit
ForWhen then the excitation of k-th array element and other array elements connect matched load in array
Active cell directional diagram is as follows：
Ek(θ, φ)=I (θ, φ) (ak+bk)=I (θ, φ) ak(1+Γk)
Wherein, I (θ, φ) is the directional diagram of an independent array element in ground level.
Further, array pattern synthesis and amendment described in step 4, it is specific as follows：
For the limited big planar array of M array element, absolute far-field pattern F (θ, φ) is as follows：
F (θ, φ)=cE (θ, φ)
WhereinC is the modifying factor of Pattern Synthesis, meets formula：
Wherein, I (θ, φ) be ground level in an independent array element directional diagram, Ek(θ, φ) is k-th of array element in array
Active cell directional diagram when excitation and other array elements connect matched load, akFor the pumping signal field strength of kth unit, bkFor kth list
The reflected signal field strength of member.
Compared with prior art, its remarkable advantage is the present invention：(1) computer CPU and request memory are reduced, emulation
Speed is fast, precision is high；(2) considering inter-element mutual coupling realizes array mutual coupling analysis, and Pattern Synthesis accuracy obtains
Improve；(3) it is not only more accurate in terms of Pattern Synthesis, and support any width of each unit mutually to encourage, suitable for oblique grid battle array
Row；(4) analyze to obtain array coupling parameter and active refelction coefficient by array mutual coupling, realize array mutual coupling analysis and direction
The synthesis of figure.
Brief description of the drawings
Fig. 1 is the theory diagram of the large-scale finite plane array analysis method of the invention based on HFSS elements methods.
Fig. 2 is HFSS elements methods simulation model-half-wave dipole rectangular grid schematic diagram.
Fig. 3 is the oblique grid schematic diagram of HFSS elements methods simulation model-half-wave dipole.
Fig. 4 is rectangle infinite matrix structural representation.
Fig. 5 is the first oblique grid infinite matrix structural representation.
Fig. 6 is second of oblique grid infinite matrix structural representation.
Fig. 7 is coupling principle figure between array antenna unit.
Fig. 8 is oblique raster plane array schematic diagram.
Fig. 9 is that 15*15 rectangular grid planar arrays are structured the formation schematic diagram.
Figure 10 is that the oblique raster plane arrays of 15*15 are structured the formation schematic diagram.
Figure 11 is 15*15 rectangular grid planar array E faces directional diagram.
Figure 12 is 15*15 rectangular grid planar array H faces directional diagram.
Figure 13 is the oblique raster plane array E faces directional diagrams of 15*15.
Figure 14 is the oblique raster plane array H faces directional diagrams of 15*15.
Figure 15 is the active cell E faces directional diagram of edge array element in rectangular grid planar array.
Figure 16 is the active cell H faces directional diagram of edge array element in rectangular grid planar array.
Figure 17 is the active cell E faces directional diagram of edge array element in oblique raster plane array.
Figure 18 is the active cell H faces directional diagram of edge array element in oblique raster plane array.
Rectangular grid planar array E faces directional diagram when Figure 19 is non-constant amplitude cophase detector.
Rectangular grid planar array H faces directional diagram when Figure 20 is non-constant amplitude cophase detector.
Figure 21 oblique raster plane array E faces directional diagrams when being non-constant amplitude cophase detector.
Figure 22 oblique raster plane array H faces directional diagrams when being non-constant amplitude cophase detector.
Embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings.
The present invention is on the basis of HFSS elements methods, it is proposed that a kind of large-scale finite plane array analysis method.This method
For comparing the emulation of full array, computer CPU and request memory are reduced and simulation velocity faster；Compare the radiation side of classical approach
To figure product theorem, it is contemplated that inter-element mutual coupling realizes array mutual coupling analysis and Pattern Synthesis accuracy is improved；
HFSS elements methods are compared, this method is not only more accurate in terms of Pattern Synthesis, and supports any width of each unit mutually to encourage, and fits
For oblique grid array, and it can realize that array mutual coupling is analyzed to obtain array coupling parameter and active refelction coefficient.
With reference to Fig. 1, the large-scale finite plane array analysis method of the invention based on HFSS elements methods, general thought is first true
Determine spacing, array between array element type, size and array element to structure the formation mode, utilize HFSS elements methods to carry out unlimited array modeling and simulating point
Analysis obtains infinite matrix active refelction coefficient, and two-dimensional FFT operation is done to infinite matrix active refelction coefficient and obtains infinite matrix coupling S ginsengs
Number, further derive and try to achieve limited battle array active refelction coefficient, in conjunction with independent array element directional diagram, element position, the width of limited battle array
Phase information is derived by the active cell directional diagram of Finite Array, and final synthesis simultaneously is corrected to obtain the synthesized pattern of array, has
Body step is as follows：
Step 1, HFSS elements methods are analyzed：Unlimited Array Model is established using HFSS elements methods, and to principal and subordinate's border surface
Between phase difference sample, emulation obtain the infinite matrix active refelction coefficient of each sampled point in a complete cycle structure.
Unlimited Array Model is established using HFSS elements methods：Single array element is modeled in electromagnetic simulation software HFSS, edge
Array grid direction and add two pairs of principal and subordinate borders to forcing field duration property to realize the infinite matrix model of planar array.
Single array element is modeled in electromagnetic simulation software HFSS, adds two pairs of principal and subordinate borders to strong along array grid direction
Field duration property processed realizes the infinite matrix model of planar array.First have to enter the single cellular of two-dimensional periodic structure in HFSS
Row Modeling Calculation, cellular selection half-wave dipole antenna structure, its centre frequency f is 3GHz, and antenna is placed along y-axis, center
Positioned at the origin of coordinates, antenna material uses perfact conductor, and total length is 0.48 λRadius
For λ/200, for antenna feed using ripple port excitation (power drive) mode, port distance be 0.24mm, mode activated solution (with
S parameter is calculated based on pattern, S parameter matrix is calculated according to the incident power of each mode field in guided wave and reflection power
Solution).Define air cartridge, it is desirable to which air box shaped is consistent with array grid shape, and air cartridge length and width are with array element in array at two
Spacing of structuring the formation on direction is consistent, and air cartridge highly meets upper and lower surface respectively apart from array element λ/4 or so, and in air cartridge surrounding
Principal and subordinate's boundary condition is set, and periodic structure is extended along array grid direction in XY faces, and spoke is set in air cartridge upper and lower surface
Penetrate boundary condition, the HFSS elements method simulation architectures model of rectangular grid and oblique grid (65.3757 degree of angle of inclination) is respectively such as
Shown in Fig. 2 and Fig. 3.
Principal and subordinate's boundary condition setting up procedure：Select a side to establish main border Master1 first in air cartridge, specify
Master1 UV vectors (consistent with array grid direction), to determine and the one-to-one relationship from border site；Choose with
Master1 opposite sides are established from border Slave1, and require the UV vector definitions requirement in Slave1 and Master1 one by one
It is corresponding；Final specified phase difference between Slave1 and Master1 is variable p1(unit：Angle).In the same way, in battle array
The other direction of row grid is established with variable p2The phase difference of definition principal and subordinate border constrained each other is to Slave2 and Master2.
There is certain phase difference in main border surface and electric field from border surface, this arbitrary boundary conditions is forced to make from border
Upper every electric field and the electric field of respective point on main border are matched with a phase difference, and the phase difference is exactly that periodic structure is adjacent
Existing phase difference between unit.One complete plan periodic structure should meet-π ＜ p1＜ π ,-π ＜ p2＜ π, to two
Phase difference p between principal and subordinate's border surface on direction1、p2Carry out N*N point samplings：
Using the method for MATLAB-HFSS associative simulations, MATLAB programs double circulation samples phase between each pair principal and subordinate border
Potential difference value is written to VB scripts, then opens electromagnetic simulation software HFSS with VB scripts and emulate to obtain under the sampling phase difference group
Infinite matrix active refelction coefficient (or infinite matrix active admittance, infinite matrix active impedance) simultaneously exports .csv files for subsequently walking
Rapid analysis.Emulated to obtain different samplings in a complete cycle structure using the method for MATLAB-HFSS associative simulations
Infinite matrix active refelction coefficient under point
Step 2, coupling analysis：Fourier transform is done to the infinite matrix active refelction coefficient under different sampled points and realizes array
Mutual Coupling Analysis, determine the coupling S parameter of infinite matrix.
Assuming that a line array, array element spacing is d, and array element infinitely extends to both sides, forms infinite matrix, then its active impedance
(input impedance of certain Single port) is
Wherein, δ is phase difference between two neighboring array element, and l is array element to be measured,It is l-th of array element and n-th in infinite matrix
Mutual impedance between individual array element.As can be seen that phase difference of the active impedance of unlimited array only between adjacent array element is relevant, by
This we can analogize the active impedance of rectangle infinite matrix as shown in Figure 4 and oblique grid infinite matrix as shown in Figure 5 just like
Lower relation：
Wherein, p and q represent respectively along any reference array element of distance in array grid both direction p-th array element and
Q-th of array element,It is exactly infinite matrix coupled impedance, δ1And δ2Represent respectively along between the adjacent array element in oblique grid both direction
Phase difference, the phase difference p between principal and subordinate border in HFSS elements methods1And p2, there is δ1=p1And δ2=p2Relation, to formula
(5) do and change, finally have
As can be seen from the above equation, the calculating process of coupled impedance is the equal of to do Two-dimensional FFT to infinite matrix active impedance, by
This can class release coupling S parameter also meet following relational expression：
It should be noted that, although coupling S parameter is different, there is such as ShiShimonoseki in Fig. 5 and Fig. 6 oblique grid infinite matrix model
System：If infinite matrix model is to set principal and subordinate's boundary condition to obtain according to oblique grid direction shown in Fig. 5 in the analysis of HFSS elements methods
A complete cycle structure in infinite matrix active refelction coefficient under different sampled pointsIf, then calculate
During the S parameter of infinite matrix model shown in Fig. 6, it is not necessary to which, again with HFSS elements methods again simulation analysis, it couples S parameter and met：
To the infinite matrix active refelction coefficient under different sampled pointsTwo-dimension fourier transform is done, it is unlimited to obtain
The coupling S parameter of battle array
Wherein, δ1、δ2Represent that p, q represent edge respectively along the phase difference between the adjacent array element in array grid both direction respectively
P-th of the array element and q-th of array element of distance reference array element in array grid both direction, N represents sampling number, sampling essence when taking 36
Degree is enough, and N is bigger, and emulation is more time-consuming, wherein
Step 3, active cell Directional Pattern Analysis：According to active cell directional diagram and the relation for coupling S parameter, with reference to independence
Array element directional diagram, the element position of limited battle array, width phase information determine active cell directional diagram.
Mutual coupling relation between array antenna unit as shown in fig. 7, set the field strength of the incoming signal of M unit in array as
ai, i=1,2 ..., M, the field strength of reflected signal is bi, i=1,2 ..., M, coefficient of coup matrix is S, in above-mentioned coupling parameter
Obtained in analysis, then have b=Sa, i.e.,
Therefore the reflected signal field strength b of kth unitkIt is represented by：
In formula, SkiRepresent the mutual coupling coefficient that i-th cell influences on kth unit, the planar array being in for front in xoy faces
Array antenna, when angle, θ is arrived in array antenna scanning0WithWhen, incoming signal field strength aiIt is represented by：
Wherein, (xi,yi) for the coordinate residing for unit i.Incoming signal field strength a can be seen that by above formulaiContain Finite Array
The amplitude-phase information of geometry, element position and array element, supports oblique grid, supports any width mutually to encourage.Kth unit has
Source reflectance factor is defined as：
Situation is fairly simple when finite plane array is rectangular grid, but when finite plane array is oblique grid, such as Fig. 8
Shown oblique raster plane array schematic diagram, appoints take an array element in an array, and array is had been partitioned into centered on the array element
Four parts, are designated as 1st quadrant, the 2nd quadrant, third quadrant and the 4th quadrant respectively, and observation is understood, 1st quadrant and third quadrant
Array mode of structuring the formation is similar with Fig. 5, and the array of the 2nd quadrant and the 4th quadrant mode of structuring the formation is similar with Fig. 6.Therefore, the 1st, 3 quadrants
Coefficient of coup matrix S1With the coefficient of coup matrix S of the 2nd, 4 quadrants2The relation of formula (6) and formula (7) be present.Calculating k-th
The active refelction coefficient Γ of unitkWhen, S in formula (11)kiValue first to judge i-th of array element centered on k-th of array element
Schematic diagram in the 1st, 3 quadrants or the 2nd, 4 quadrants, so just can determine that SkiIt is S1kiOr S2kiIn substitution formula.
Active cell directional diagram refers in array environment, only encourages a reference unit and other units connect matched load
When far-field pattern, then the active cell directional diagram of kth element excitation is in array：
Ek(θ, φ)=I (θ, φ) (ak+bk)=I (θ, φ) ak(1+Γk) (12)
Wherein I (θ, φ) is the directional diagram of an independent array element in ground level, and independent array element directional diagram can be in Electromagnetic Simulation
Establish an independent array element model in software HFSS, define air cartridge, and ensure air cartridge surrounding apart from array element λ/4 or so,
In air cartridge plus radiation boundary condition emulates to obtain.
Step 4, array pattern synthesis and amendment：Integrated active element pattern, and synthesis result is modified most
Synthesized pattern is obtained eventually.
For a Finite Array, the synthesized pattern of array can be by each element excitation all units encourage simultaneously when
Caused antenna pattern weighted sum obtains
Due to the influence of graing lobe being likely to occur in real space, the absolute value of crest is difficult accurately to obtain.When array without
When limiting big, main beam and graing lobe are made up of impulse function, and now radiant power is divided into many impulse functions, the gain of main beam
It will be reduced (for example, the increased situation of unit spacing) with the increase of graing lobe in real space.But if array is limited big
When, situation will become more complicated.When an array is made up of limited individual array element, with the increase of array element spacing, it is seen that
More graing lobes will occur in space, but main beam and secondary lobe can narrow with the increase in aperture simultaneously.Both shadows
Sound often cancels each other so that the absolute gain of crest keeps constant.In addition, for the Finite Array of a finite bandwidth, grid
Valve is not to be regarded as simply in real space and not in real space, and before side lobe peak is visible, they are deviateing
Gradually start to occur during 90 degree of main beam.Because above-mentioned reason, for a Finite Array, what is most insured is exactly to enter in preceding hemisphere
Line direction figure integrates to obtain absolute far-field pattern F (θ, φ)
F (θ, φ)=cE (θ, φ) (14)
Wherein c is the modifying factor that Pattern Synthesis obtains, and is obtained by numerical integration
The directivity factor of array is obtained by following formula
And array overall gain is as follows
Embodiment 1
The rectangular grid planar array for mode that simulation model in Fig. 2 is structured the formation by above-mentioned thinking simulation analysis as shown in Figure 9,
In order to ensure simulation accuracy, during the analysis of HFSS elements methods, phase difference takes 5 degree one to be spaced between principal and subordinate's border surface, and 36*36 is adopted
Sample.It is final to analyze the coupling S parameter for obtaining the array, active cell directional diagram, absolute far-field pattern etc..It will be imitated again in Fig. 3
True mode is structured the formation the oblique raster plane array of mode as shown in Figure 10 by above-mentioned thinking simulation analysis, and sampled point equally takes 5 degree one
Interval, 36*36 samplings are final to analyze the coupling S parameter for obtaining the oblique grid array, active cell directional diagram, absolute far field side
To figure etc..
Will be with the identical half-wave dipole antenna of simulation model size in Fig. 2 and Fig. 3 in XOY plane difference cloth 15*
15 rectangular grid planar array and oblique raster plane array, the array element spacing air cartridge with simulation model in Fig. 2 and Fig. 3 respectively
Size is completely the same, structures the formation mode as shown in Figure 9 and Figure 10, establishes full Array Model respectively in electromagnetic simulation software HFSS,
Surrounding adds an air cartridge, and whole air cartridge adds radiation boundary condition, and full array emulation is carried out in HFSS, finally emulates
To the mutual coupling S parameter of center array element, active cell directional diagram, absolute far-field pattern etc..
(1) simulation time comparative result
The emulation of table 1 is time-consuming to compare
| Rectangular grid array | Oblique grid array | |
| Full array emulation | 45h | 46h |
| The solution of the present invention | 30h | 31.4h |
The solution of the present invention as can be seen from Table 1, for being emulated compared to more full array, simulation velocity has obtained greatly carrying
It is high.Importantly, when array elements number improves, complete the time-consuming of array emulation will be longer, persistently increases in array element number
In the case of, or even calculator memory occur and not enough imitate motionless situation；And the solution of the present invention, as long as not increasing sampled point
Number (it is demonstrated experimentally that 36*36 sampling precision is enough), the same great array simulation time of array element model cloth is all fixed
, and in the absence of the inadequate situation of calculator memory.As can be seen here, the solution of the present invention is compared with full array emulates, to meter
The CPU and request memory of calculation machine be not high, and simulation velocity is faster.
(2) S parameter comparative result is coupled
The rectangular grid array of table 2 coupling S parameter simulation result compares
3 oblique grid array of table coupling S parameter simulation result compares (a)
4 oblique grid array of table coupling S parameter simulation result compares (b)
Table 1 is the results contrast that two methods calculate rectangular grid array center's array element coupling S parameter (＞ -45dB), can
To find out, the result of two methods is coincide very much, as a result poor to be no more than 0.22dB, is demonstrated the solution of the present invention and is calculated rectangle grid
Lattice array couples the validity and accuracy of S parameter.
Table 3 and table 4 are all the result ratios that two methods calculate oblique grid array center array element coupling S parameter (＞ -45dB)
Compared with, unlike, table 3 is the coupling S parameter of the 1st, 4 quadrant correspondence position relations in similar Fig. 8, table 4 is the 2nd in similar Fig. 8,
The coupling S parameter of 3 quadrant correspondence position relations.Observation understands that no matter, table 3 or table 4, the result of two methods is also all extremely kissed
Close, as a result difference is not no more than 0.31dB and 0.51dB, demonstrates the solution of the present invention and calculates oblique grid array and couples S parameter
Validity and accuracy.
(3) absolute far-field pattern comparative result during constant amplitude cophase detector
Figure 11 and Figure 12 is the E faces and H faces of the absolute far-field pattern of rectangular grid planar array, wherein solid black lines respectively
The result of full array emulation is represented, zero line is the simulation result of the solution of the present invention, and black × line represents the imitative of HFSS elements methods
True result, black dotted lines represent not considering the simple result that the directional diagram product theorem of mutual coupling calculates.As can be seen from Figure,
Solid black lines and the fitting of zero line are best, demonstrate the solution of the present invention in terms of the Pattern Synthesis of rectangular grid planar array
Validity and accuracy.
Figure 13 and Figure 14 is the E faces and H faces of the oblique absolute far-field pattern of raster plane array respectively, with Figure 11 and Figure 12 classes
Seemingly, it can clearly find out that solid black lines and zero line fit solution are best from figure, demonstrate the solution of the present invention and put down in oblique grid
Validity and accuracy in terms of the Pattern Synthesis of face array.
(4) active cell directional diagram comparative result
Figure 15 and Figure 16 is the active cell side of edge array element B (as shown in Figure 9) in rectangular grid planar array respectively
To the E faces and H faces of figure, solid black lines are full array simulation results, and black dotted lines are the simulation results of the present invention, and two lines are fitted
It is all right, demonstrate the validity that the present invention calculates active cell directional diagram in rectangular grid planar array.
Figure 17 and Figure 18 is the active cell direction of edge array element A (as shown in Figure 10) in oblique raster plane array respectively
The E faces and H faces of figure, similar with Figure 17 and Figure 18, two lines fit solution is good, demonstrates the present invention and calculates oblique raster plane battle array
The validity of active cell directional diagram in row.
HFSS elements methods and simple directional diagram product theorem can not obtain the active cell directional diagram of array, and this also illustrates
Superiority of the present invention program compared to other method.
(5) far-field pattern comparative result during non-constant amplitude cophase detector
The non-constant amplitude cophase detector situation of table 5
| Element position | Amplitude/W | Phase/deg |
| A | 16 | 60 |
| B | 4 | 60 |
| C | 4 | 40 |
| D | 16 | 40 |
| E | 8 | 60 |
| F | 8 | 20 |
| G | 4 | 10 |
Note：Corresponded in element position A, B, C, D, E, F, G and Fig. 9 and Figure 10；
When Figure 19 and Figure 20 is the non-constant amplitude cophase detector of situation according to table 5 respectively, rectangular grid planar array far field side
To the E faces and H faces of figure, wherein solid black lines are the results of full array emulation, and black dotted lines are the simulation results of the present invention program,
It can be seen that two lines fit solution is fine, demonstrate the solution of the present invention when emulating rectangular grid planar array support it is non-etc.
The Pattern Synthesis of width cophase detector.
When Figure 21 and Figure 22 is the non-constant amplitude cophase detector of situation according to table 5 respectively, oblique raster plane array far field direction
The E faces and H faces of figure, similar with Figure 19 and Figure 20, two lines fit solution is also fine, demonstrates and is emulating oblique raster plane array
When the solution of the present invention support the Pattern Synthesis of non-constant amplitude cophase detector.
(6) conclusion
Knowable to 5 comparisons of summary, the large-scale finite plane array analysis based on HFSS elements methods of the invention pointed out
Method has the advantages of not high to computer CPU and request memory, simulation velocity is fast compared with full array emulates；With other emulation
Method is compared, and coupling make it that simulation accuracy is high between it considers unit, and is applied to oblique grid array, supports any width of each unit
Mutually encourage, active refelction coefficient in array, active cell directional diagram etc. can be obtained.
Claims (5)
- A kind of 1. large-scale finite plane array analysis method based on HFSS elements methods, it is characterised in that step is as follows：Step 1, HFSS elements methods are analyzed：Unlimited Array Model is established using HFSS elements methods, and phase principal and subordinate's border surface Potential difference samples, and emulation obtains the infinite matrix active refelction coefficient of each sampled point in a complete cycle structure；Step 2, coupling analysis：Fourier transform is done to the infinite matrix active refelction coefficient under different sampled points and realizes the mutual of array Coupling is analyzed, and determines the coupling S parameter of infinite matrix；Step 3, active cell Directional Pattern Analysis：According to active cell directional diagram and the relation for coupling S parameter, with reference to independent array element Directional diagram, the element position of limited battle array, width phase information determine active cell directional diagram；Step 4, array pattern synthesis and amendment：Integrated active element pattern, and final obtain is modified to synthesis result To synthesized pattern.
- 2. the large-scale finite plane array analysis method according to claim 1 based on HFSS elements methods, it is characterised in that HFSS elements methods described in step 1 are analyzed, specific as follows：(1.1) unlimited Array Model is established using HFSS elements methods：Single array element is modeled in electromagnetic simulation software HFSS, edge Array grid direction and add two pairs of principal and subordinate borders to forcing field duration property to realize the infinite matrix model of planar array；(1.2) phase difference p principal and subordinate's border surface in both direction1、p2Carry out N*N point samplings：<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mrow> <mn>1</mn> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mi>&pi;</mi> <mfrac> <mi>n</mi> <mi>N</mi> </mfrac> </mrow> </mtd> <mtd> <mrow> <mi>n</mi> <mo>=</mo> <mo>-</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mo>,</mo> <mo>-</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mo>-</mo> <mn>2</mn> <mo>,</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced><mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mi>&pi;</mi> <mfrac> <mi>m</mi> <mi>N</mi> </mfrac> </mrow> </mtd> <mtd> <mrow> <mi>m</mi> <mo>=</mo> <mo>-</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mo>,</mo> <mo>-</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mo>-</mo> <mn>2</mn> <mo>,</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced>(1.3) emulated to obtain different samplings in a complete cycle structure using the method for MATLAB-HFSS associative simulations Infinite matrix active refelction coefficient under point
- 3. the large-scale finite plane array analysis method according to claim 1 based on HFSS elements methods, it is characterised in that The detailed process of coupling analysis described in step 2 is as follows：To the infinite matrix active refelction coefficient under different sampled pointsTwo-dimension fourier transform is done, obtains infinite matrix Couple S parameter<mrow> <msubsup> <mi>S</mi> <mrow> <mi>p</mi> <mi>q</mi> </mrow> <mi>&infin;</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>*</mo> <mi>N</mi> </mrow> </mfrac> <munder> <mo>&Sigma;</mo> <mi>n</mi> </munder> <munder> <mo>&Sigma;</mo> <mi>m</mi> </munder> <msubsup> <mi>S</mi> <mrow> <mi>A</mi> <mi>C</mi> <mi>T</mi> </mrow> <mi>&infin;</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>&delta;</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>&delta;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mrow> <mo>(</mo> <msub> <mi>&delta;</mi> <mn>1</mn> </msub> <mi>p</mi> <mo>+</mo> <msub> <mi>&delta;</mi> <mn>2</mn> </msub> <mi>q</mi> <mo>)</mo> </mrow> </mrow> </msup> </mrow>Wherein, δ1、δ2Represent that p, q represent edge respectively along the phase difference between the adjacent array element in array grid both direction respectively P-th of the array element and q-th of array element of distance reference array element in array grid both direction, N represents sampling number, wherein
- 4. the large-scale finite plane array analysis method according to claim 1 based on HFSS elements methods, it is characterised in that Active cell Directional Pattern Analysis described in step 3, it is specific as follows：For the limited big planar array of a M array element, the field strength of the pumping signal of M unit is a in arrayi, i=1, 2 ..., M, consider the mutual coupling between each antenna element, the reflected signal field strength b of kth unitkIt is expressed as：<mrow> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>S</mi> <mrow> <mi>k</mi> <mi>i</mi> </mrow> </msub> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>,</mo> <mrow> <mo>(</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>M</mi> <mo>)</mo> </mrow> </mrow>In formula, SkiIt is to reflect the mutual coupling coefficient that i-th cell influences on kth unit；The active refelction coefficient of kth unit is defined asK=1,2 ..., M, then it is active when the excitation of k-th array element and other array elements connect matched load in array Element pattern is as follows：Ek(θ, φ)=I (θ, φ) (ak+bk)=I (θ, φ) ak(1+Γk)Wherein, I (θ, φ) is the directional diagram of an independent array element in ground level.
- 5. the large-scale finite plane array analysis method according to claim 1 based on HFSS elements methods, it is characterised in that Array pattern synthesis and amendment, specific as follows described in step 4：For the limited big planar array of M array element, absolute far-field pattern F (θ, φ) is as follows：F (θ, φ)=cE (θ, φ)WhereinC is the modifying factor of Pattern Synthesis, meets formula：<mrow> <mfrac> <mrow> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> </msubsup> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mfrac> <mi>&pi;</mi> <mn>2</mn> </mfrac> </msubsup> <mo>|</mo> <mi>c</mi> <mi>E</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>,</mo> <mi>&phi;</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&theta;</mi> <mi>d</mi> <mi>&phi;</mi> </mrow> <mrow> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> </msubsup> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mfrac> <mi>&pi;</mi> <mn>2</mn> </mfrac> </msubsup> <mo>|</mo> <mi>I</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>,</mo> <mi>&phi;</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&theta;</mi> <mi>d</mi> <mi>&phi;</mi> </mrow> </mfrac> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <mo>|</mo> <msub> <mi>a</mi> <mi>k</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <mo>|</mo> <msub> <mi>b</mi> <mi>k</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow>Wherein, I (θ, φ) be ground level in an independent array element directional diagram, Ek(θ, φ) be in array the excitation of k-th array element and Other array elements meet active cell directional diagram during matched load, akFor the pumping signal field strength of kth unit, bkFor the anti-of kth unit Penetrate signal strength.
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